Measurement and Significant Figures

Measurement andSignificant Figures www.lab-initio.com

Steps in the Scientific Method • 1. Observations • - quantitative • - qualitative • 2. Formulating hypotheses • - possible explanation for the observation • 3. Performing experiments • - gathering new information to decide whether the hypothesis is valid

Outcomes Over the Long-Term • Theory (Model) • - A set of tested hypotheses that give an overall explanation of some natural phenomenon. • Natural Law • - The same observation applies to many different systems

Law vs. Theory A law summarizes what happens A theory (model) is an attempt to explain why it happens. Einstein's theory of gravity describes gravitational forces in terms of the curvature of spacetime caused by the presence of mass

Nature of Measurement A measurement is a quantitative observation consisting of 2 parts: • Part 1 - number • Part 2 - scale (unit) • Examples: • 20 grams • 6.63 x 10-34Joule·seconds

The Fundamental SI Units(le Système International, SI)

SI Units

Celsius & Kelvin

SI Prefixes Common to Chemistry

Uncertainty in Measurement • A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty. • Measurements are performed with instruments • No instrument can read to an infinite number of decimal places

Precision and Accuracy • Accuracy refers to the agreement of a particular value with the true value. • Precision refers to the degree of agreement among several measurements made in the same manner. Precise but not accurate Precise AND accurate Neither accurate nor precise

Types of Error • Random Error(Indeterminate Error) - measurement has an equal probability of being high or low. • Systematic Error(Determinate Error) - Occurs in the same direction each time (high or low), often resulting from poor technique or incorrect calibration. This can result in measurements that are precise, but not accurate.

Rules for Counting Significant Figures - Details • Nonzero integersalways count as significant figures. • 3456has • 4 sig figs.

Rules for Counting Significant Figures - Details • Zeros • - Leading zeros do not count as significant figures. • 0.0486has • 3sig figs.

Rules for Counting Significant Figures - Details • Zeros • - Captive zerosalways count as significant figures. • 16.07has • 4sig figs.

Rules for Counting Significant Figures - Details • Zeros • Trailing zeros are significant only if the number contains a decimal point. • 9.300has • 4sig figs.

Rules for Counting Significant Figures - Details • Exact numbershave an infinite number of significant figures. • 1inch=2.54cm, exactly

Sig Fig Practice #1 How many significant figures in each of the following? 1.0070 m  5 sig figs 17.10 kg  4 sig figs 100,890 L  5 sig figs 3.29 x 103 s  3 sig figs 0.0054 cm  2 sig figs 3,200,000  2 sig figs

Rules for Significant Figures in Mathematical Operations • Multiplication and Division: • # sig figs in the result equals the number in the least precise measurement used in the calculation. • 6.38 x 2.0 = • 12.76 13 (2 sig figs)

Sig Fig Practice #2 Calculation Calculator says: Answer 22.68 m2 3.24 m x 7.0 m 23 m2 100.0 g ÷ 23.7 cm3 4.22 g/cm3 4.219409283 g/cm3 0.02 cm x 2.371 cm 0.05 cm2 0.04742 cm2 710 m ÷ 3.0 s 236.6666667 m/s 240 m/s 5870 lb·ft 1818.2 lb x 3.23 ft 5872.786 lb·ft 2.9561 g/mL 2.96 g/mL 1.030 g ÷ 2.87 mL

Rules for Significant Figures in Mathematical Operations • Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement. • 6.8 + 11.934 = • 18.734  18.7(3 sig figs)

Sig Fig Practice #3 Calculation Calculator says: Answer 10.24 m 3.24 m + 7.0 m 10.2 m 100.0 g - 23.73 g 76.3 g 76.27 g 0.02 cm + 2.371 cm 2.39 cm 2.391 cm 713.1 L - 3.872 L 709.228 L 709.2 L 1821.6 lb 1818.2 lb + 3.37 lb 1821.57 lb 0.160 mL 0.16 mL 2.030 mL - 1.870 mL

Measurement and Significant Figures